Hida 族中的经典权一形式：Hilbert 模情形
数论
2016-11-07 v2
摘要
本文旨在研究平行权 Hilbert 尖点形式的非 CM 普通 Hida 族的经典权一特化的个数。已知本原普通 Hida 族在权至少为二的任意算术点处的特化是经典全纯 Hilbert 尖点形式。然而，对于权一特化，情况并非总是如此。Balasubramanyam、Ghate 和 Vatsal 证明了这样的 Hida 族当且仅当其为 CM 型时才允许无穷多个经典权一特化。我们给出了非 CM 本原普通 Hida 族的经典权一特化个数的一个显式上界。
引用
@article{arxiv.1606.06554,
title = {Classical weight one forms in Hida families: Hilbert modular case},
author = {Tomomi Ozawa},
journal= {arXiv preprint arXiv:1606.06554},
year = {2016}
}
备注
18 pages. Comments welcome. v2: eliminated the assumption that there exists an integral free lattice of the Galois representation attached to a Hida family (it was not necessary), added a detailed description of the residual Galois representation in Section 2.3